Question

What should be the maximum speed with which a car can be driven through a curve of radius $18m$ without skidding (where, $g=10m{s}^{-2}$, coefficient of static friction between the rubber tyres and the roadway is $0.2$)?

• A. $36.0km{h}^{-1}$
• B. $18.0km{h}^{-1}$
• C. $21.6km{h}^{-1}$
• D. $14.4km{h}^{-1}$

Answer 1

The correct option is C $21.6km{h}^{-1}$

Given, $r=18m,g=10m{s}^{-2}$
and $\mu =0.2$
Equation for dynamics of circular motion gives:
$\frac{m{v}_{max}^2}{r}=f={\mu }_{s}N={\mu }_{s}mg$
$v_{max}=\sqrt{{\mu }_{s}rg}=\sqrt{0.2\times 18\times 10}=6m{s}^{-1}$
Or, $6\times \frac{18}{5}km{h}^{-1}=21.6km{h}^{-1}$